1/6x-5/6=1/2x+3

Solution for 1/6x-5/6=1/2x+3 equation:

1/6x-5/6=1/2x+3

We move all terms to the left:

1/6x-5/6-(1/2x+3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

1/6x-1/2x-3-5/6=0

We calculate fractions


2x/432x^2+(-216x)/432x^2+(-10x)/432x^2-3=0

We multiply all the terms by the denominator


2x+(-216x)+(-10x)-3*432x^2=0

Wy multiply elements

-1296x^2+2x+(-216x)+(-10x)=0

We get rid of parentheses

-1296x^2+2x-216x-10x=0

We add all the numbers together, and all the variables

-1296x^2-224x=0

a = -1296; b = -224; c = 0;
Δ = b2-4ac
Δ = -2242-4·(-1296)·0
Δ = 50176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50176}=224$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-224}{2*-1296}=\frac{0}{-2592}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+224}{2*-1296}=\frac{448}{-2592}
=-14/81
$